Vertical Contracting Between Airlines: An Equilibrium Analysis
of Codeshare Alliances∗
Yongmin Chen† Philip G. Gayle‡
University of Colorado at Boulder Kansas State University
This paper studies the competitive eﬀects of airline codeshare alliances. We consider an
airline market with two ﬁrms oﬀering two diﬀerentiated ﬁnal products: a direct ﬂight and an
indirect ﬂight between two destinations. An intermediate (complementary) ﬂight is needed to
complete the indirect ﬂight. When the intermediate ﬂight is oﬀered only by a third airline,
codesharing between the two complementary airlines eliminates double markup and lowers con-
sumer prices. When the intermediate ﬂight is oﬀered only by the airline that also oﬀers the
direct ﬂight, codesharing does not eliminate the double markup, but, interestingly, it again low-
ers ﬁnal prices for consumers. However, if both the third and the direct-ﬂight airlines can oﬀer
the intermediate ﬂight, then allowing codesharing leads to the exclusion of the third airline and
to higher consumer prices.
JEL Classiﬁcation: L13, L93
Keywords: Codeshare Alliance, Airline Pricing, Vertical Contracting.
We have beneﬁtted from the helpful comments of a referee.
Department of Economics, University of Colorado at Boulder, Boulder, CO 80309 , Tel: (303)492-8736, email:
Department of Economics, 320 Waters Hall, Kansas State University, Manhattan, KS, 66506. Tel. (785) 532-4581,
Fax: (785) 532-6919, email: firstname.lastname@example.org.
Codeshare alliances between major U.S. airlines have become increasingly popular over the last
decade.1 This has led to much discussion among economists and policy makers about the eﬀects of
codesharing on competition and consumer welfare.2 A prevalent view is that codesharing eliminates
double marginalization and hence reduces market prices (Brueckner and Whalen, 2000; Brueckner,
2001; Brueckner, 2003; Bamberger, Carlton, and Neumann, 2004; and Ito and Lee, 2007). This
result is predicated on the logic that partners jointly price their codeshare products and therefore
will price the intermediate product of any partner airline at the true marginal cost.3
In this paper, we provide an equilibrium analysis of the pricing behavior and competitive eﬀects
of a codesharing alliance. While we maintain the same assumption as in the theoretical literature
that airlines forming a codesharing alliance will jointly price their products, we do not presume
that this leads to marginal cost pricing for an intermediate good (ﬂight) in the alliance. Rather, we
study the equilibrium pricing incentives for partners in the alliance, and consider the endogenous
formation of the alliance when multiple airlines can potentially oﬀer the intermediate ﬂight. We
ﬁnd that codesharing may or may not eliminate double marginalization, depending on whether a
codeshare partner also oﬀers a single-carrier product in the concerned market. Speciﬁcally, if no
codeshare partner oﬀers a single-carrier product, then codesharing indeed leads to true marginal
cost pricing for the intermediate good and lowers ﬁnal prices; otherwise, codesharing does not
eliminate double marginalization, and can result in higher market prices.
Codesharing combines the operating services of at least two separate carriers, where only one
of the carriers is responsible for marketing and setting the ﬁnal price for the entire round-trip
ticket ("ticketing carrier") and compensating the other carrier ("operating carrier") for their pure
operating services on a segment of the trip.4 For example, in traveling from Hartford, Connecticut,
For example, U.S. domestic alliances include, United Airlines with US Airways, American Airlines with Alaska
Airlines, and Delta Air Lines with Northwest Airlines and Continental Airlines.
For policy discussions on the potential eﬀects of codeshare alliances see, “Aviation Competition: Eﬀects on
Consumers From Domestic Airline Alliances Vary,” Report # GAO/RCED-99-37, U.S. General Accounting Oﬃce
(1999); and “Termination of review under 49U.S.C. § 41720 of Delta/Northwest/Continental Agreements”, U.S.
Department of Transportation, Oﬃce of the Secretary (2003).
We are concerned with alliances in which partners’ routes are complementary; i.e., the codesharing is a form of
vertical contracting. If partners’ route network overlap prior to formation of the alliance, the alliance is typically
referred to as parallel, which tends to have the eﬀect of softening competition and raising market prices (see Park,
1997; Park, Zhang, and Zhang, 2001; Brueckner and Whalen, 2000; Brueckner, 2001; and Gayle, forthcoming).
Within the U.S. domestic market sometimes a ticketing carrier of a product does not provide any operating
services for the product. This is referred to as "Virtual" codesharing (see Ito and Lee, 2007; and Gayle, 2007). We
do not consider such agreements in our analysis.
to Houston, Texas a passenger may have bought the codeshare round-trip ticket from Northwest
Airlines, but the itinerary involves ﬂying on Northwest Airlines from Hartford to Detroit, Michigan,
then connecting to a Continental Airlines ﬂight from Detroit to Houston. We can therefore
consider codesharing as a vertical contract between ticketing and pure operating carriers. The
pure "operating carrier" is equivalent to an upstream supplier that provides an essential input
(operate a trip segment) to the downstream "ticketing carrier" who then combines it with other
inputs (complementary trip segments) in order to provide the ﬁnal product to consumers.
In the example above, Continental Airlines also oﬀers non-stop round-trip service between
Hartford and Houston. This implies that, in addition to being an “upstream” codesharing partner
for the interline product (where a passenger changes airlines at an intermediate stop), Continental is
also a vertically integrated ﬁrm in this market. In fact, unlike codeshare alliances between diﬀerent
national carriers,5 it is common for a U.S. codeshare partner to oﬀer both interline connecting
service and competing single-carrier service within the same origin-destination market. In a data
set that spans 155 U.S. domestic markets, Gayle (2006) found that close to half (44%) of the interline
codeshare products are oﬀered by pure operating carriers that simultaneously oﬀer competing single-
carrier products. This feature of a codesharing partner, together with whether there is competition
for the “intermediate good” in the indirect-ﬂight product, turns out to be crucial in determining
the eﬀects of codesharing alliances. As we shall demonstrate, in the presence of a codesharing
partner who also oﬀers a direct ﬂight, the price for the codesharing intermediate good will exceed
its marginal cost; but, if there is no other ﬁrm oﬀering the intermediate good, the ﬁnal prices
will still be below what they would be without codesharing. However, if there is another ﬁrm
oﬀering the intermediate good, then allowing codesharing raises ﬁnal prices and harms consumers.
The reason for this last result is that, with codesharing, the ﬁrm oﬀering the direct ﬂight (the
“vertically integrated” ﬁrm) will be able to exclude competition for the intermediate good in the
indirect ﬂight. This happens because a ticketing carrier will strategically choose to codeshare with
a vertically integrated operating carrier in an eﬀort to soften downstream competition; and the
vertically integrated operating carrier will indeed compete less aggressively downstream since it
takes into account the proﬁt from its intermediate good in the codesharing product.6
For example, American Airlines, British Airways, Finnair, among others are part of the OneWorld alliance, while
United, Lufthansa, Air Canada, among others form the Star Alliance.
This is related to the idea in several recent papers in other contexts; see Chen (2001), Chen and Riordan
(forthcoming), and Sappington (2005).
The rest of the paper is organized as follows. Section 2 presents our model of an airline market
with two ﬁrms oﬀering two diﬀerentiated ﬁnal products: a direct ﬂight and an indirect (interline)
ﬂight between two destinations. To complete the indirect ﬂight, an intermediate (complementary)
ﬂight is needed. The intermediate ﬂight is oﬀered either by a third airline or/and by the airline
who is also oﬀering the direct ﬂight. Section 3 studies market equilibrium when only the third
airline oﬀers the intermediate ﬂight (in this case, each of the three airlines oﬀers a single product).
Section 4 studies market equilibrium when airline 1 oﬀers both a direct ﬂight and the intermediate
ﬂight to the other airline, but no other airline oﬀers the intermediate ﬂight. Section 5 studies
market equilibrium when a third airline and the direct-ﬂight airline both oﬀer the intermediate
good for the indirect-ﬂight product. Section 6 concludes. A linear-demand example is presented
in the appendix.
2 The Model
A market is deﬁned as round-trip air travel between an origin and a destination city. A ﬂight
itinerary is deﬁned as a speciﬁc sequence of airport stops in traveling from the origin to the desti-
nation city. Products are deﬁned as a unique combination of airline(s) and ﬂight itinerary.
Our model has up to three airlines, A1, A2, and A3, and three cities, X, Y, and Z. A1 provides
non-stop round-trip service between cities X and Z; A2 provides non-stop round-trip service between
cities Y and Z; and either A1 or/and A3 provide non-stop round-trip service between cities X and
Y. Figure 1 depicts each airlines’ route(s) between the cities.
X Airline A1
Our focus is on the origin-destination market X-Z. Based on Figure 1, a passenger travelling
between X and Z has two diﬀerentiated products to choose from: a direct-ﬂight itinerary on A1,
D; and a non-direct itinerary N with one intermediate stop in city Y using airlines A2 and Au,
where u = either 1 or 3. We can consider product N as consisting of two complementary goods,
nxy and nyz . Thus, there are three possible market structures under our consideration: only A1
oﬀers nxy , only A3 oﬀers nxy , and both A1 and A3 oﬀer nxy . Notice that when u = 1, A1 is oﬀering
both D and an intermediate product to A2, and we use M to denote this (multi-product for A1)
market structure. When u = 3, each airline is oﬀering a single product, and we use S to denote
this (single-product) market structure.7 When both A1 and A3 oﬀer nxy , the market structure is
denoted as B.
Let pD and pN be the ﬁnal prices for the two products (itineraries). Consumer demands for
these two products are assumed to be
qD (pD , pN ) and qN (pD , pN ) , where
¯ ¯ ¯ ¯
∂qi ∂qi ¯ ∂qi ¯ ¯ ∂qi ¯
<0< and ¯¯ ¯<¯ ¯ , for i, j = D, N, and i 6= j.
∂pi ∂pj ∂pj ¯ ¯ ∂pi ¯
Thus, as is usually assumed in the literature, demand for a product is decreasing in its own price but
increasing in the other product’s (substitute’s ) price; and demand is more sensitive with respect
to its own price change than to price change of the other product.
Under either market structure S or M , there are two potential pricing regimes for Au (u = 1
or 3) and A2.8 Without codesharing, Au and A2 choose their prices, ru and r2 , independently. In
this case, pN = ru + r2 . With codesharing, A2 will set the price for the entire itinerary, pN , and
pay Au a per-ticket price wu in addition to a ﬁxed payment tu . For convenience, we assume that
nxy is a homogeneous product, whether it is produced by A1 or A3.
Constant marginal costs are cD ≥ 0 for D, cxy ≥ 0 for good nxy , and cyz ≥ 0 for good nyz . In
addition, there are possibly ﬁxed costs: kD ≥ 0 for producing D, kxy ≥ 0 for nxy and kyz ≥ 0 for
nyz if there is no codesharing, and kxyz ≥ 0 for N if there is codesharing. We assume that none of
the ﬁxed costs is so large as to cause any airline to incur negative proﬁts by being in the market.
Equivalently, we may consider that A1 produces D, a vertically integrated product, while Au produces an essential
input for A2 who produces N.
Under market structure B, there is also the issue of which airline, A1 or A3, will be chosen to codeshare with
A2. We shall analyze market structure B in Section 5.
The timing of the game under market structures M and S is as follows:
Without codesharing alliance, A1, A2, and Au simultaneously choose pD , r2 , and ru .
With codesharing, Au and A2 ﬁrst negotiate a private contract (wu , tu ). A1 and A2 then
simultaneously choose pD and pN .
Market structure M or S, together with or without codesharing, leads to the following four
possible combinations of market structure and contracting: (i) Only A3 oﬀers nxy and there is no
codesharing; (ii) Only A3 oﬀers nxy but there is codesharing between nxy and nyz ; (iii) Only A1
oﬀers nxy and there is no codesharing; (iv) Only A1 oﬀers nxy but there is codesharing between
nxy and nyz . In each case, we shall assume that a ﬁrm’s proﬁt is concave in its own price(s) in
the relevant ranges of parameter values, prices are strategic complements (i.e., a ﬁrm’s marginal
proﬁt in a price increases in other prices), and there exists a unique and stable equilibrium. This
amounts to assuming that the reaction curves deﬁned by the ﬁrst-order conditions are upward
slopping and have a unique intersecting point (i.e., a unique equilibrium), and that an increase in a
reaction function will result in a new equilibrium with higher prices. This will allow us to compare
equilibrium prices under diﬀerent market structures and contracting possibilities.9
3 When Only A3 Oﬀers nxy
This situation corresponds to market structure S, with each ﬁrm oﬀering a single product (i.e.,
u = 3).
3.1 No Codesharing
We ﬁrst study the market equilibrium when there is no codesharing between A2 and A3. Without
codesharing, A1, A2, A3 simultaneously choose prices pD , r2 , and r3 . Let pN = r2 +r3 . The variable
proﬁts of the three ﬁrms are, respectively:
π 1 = (pD − cD ) qD (pD , pN ) , π 2 = (r2 − cyz ) qN (pD , pN ) , π 3 = (r3 − cxy ) qN (pD , pN ) .
These assumptions are admittedly strong, and are made to minimize technical details that are not essential
for our results. In the Appendix, we give a linear-demand example in which all assumptions are satisﬁed. Similar
assumptions are made in the literature, as, for instance, in Ordover, Saloner, and Salop (1990) and Chen (2001).
The equilibrium prices, pS , r2 , r3 , satisfy the following ﬁrst-order conditions:
∂qD (pD , pN )
qD (pD , pN ) + (pD − cD ) = 0, (1)
∂qN (pD , pN )
qN (pD , pN ) + (r2 − cyz ) = 0, (2)
∂qN (pD , pN )
qN (pD , pN ) + (r3 − cxy ) = 0, (3)
and we let pS = r2 + r3 . These ﬁrst-order conditions implicitly deﬁne three reaction functions.
Adding equations (2) and (3), we obtain
∂qN (pD , pN )
2qN (pD , pN ) + (pN − cxy − cyz ) = 0. (4)
Equations (1) and (4) implicitly deﬁne the functions of two upward-slopping reaction curves in the
pD -pN space:
pD = RD (pN ) , pN = RN (pD ) .
Therefore, the equilibrium prices pS , pS solve equations (1) and (4), with
S pS − cxy + cyz
N S pS + cxy − cyz
r2 = , r3 = .
It follows that r2 − cyz = r3 − cxy , or the two complementary goods have the same markups. The
equilibrium variable proﬁts are
¡ ¢ ¡ ¢ ¡ S ¢ ¡ ¢ ¡ S ¢ ¡ ¢
π S = pS − cD qD pS , pS ,
1 D D N π S = r2 − cyz qN pS , pS ,
2 D N π S = r3 − cxy qN pS , pS .
3 D N
3.2 Comparing With Codesharing
We next consider the equilibrium when there is codesharing between A2 and A3. In this case, A3
and A2 ﬁrst negotiate a private contract (w3 , t3 ). A1 and A2 then simultaneously choose pD and
pN . When A3 and A2 form a codesharing alliance, we follow the existing theoretical literature and
assume that they will choose w3 to maximize their joint proﬁts, which implies that w3 will equal
to the true marginal cost of nxy , 10 or w3 = cxy . The equilibrium value of t3 will depend on speciﬁc
assumptions on the bargaining process. For the purpose of this paper, we do not need to know
how the surplus is distributed between A3 and A2 through the ﬁxed transfer payment, which does
not aﬀect the equilibrium choices of pD and pN . Provided that codesharing increases the partners’
joint proﬁts so that there is incentive to form the alliance, all we need to know is the equilibrium
Thus, as in the literature, when each ﬁrm oﬀers a single product, codesharing indeed eliminates double markup.
per-unit price for the intermediate good under codesharing, and the resulting equilibrium ﬁnal
prices. We shall follow this approach for the rest of the paper when we analyze equilibrium under
The variable proﬁt of A1 and the joint variable proﬁt of A2 and A3 are, respectively:
π 1 = (pD − cD ) qD (pD , pN ) , π 23 = (pN − cxy − cyz ) qN (pD , pN ) .
The equilibrium prices, pSC , pSC , solve the ﬁrst-order conditions:
∂qD (pD , pN )
qD (pD , pN ) + (pD − cD ) = 0, (5)
∂qN (pD , pN )
qN (pD , pN ) + (pN − cxy − cyz ) = 0, (6)
which implicitly deﬁne two reaction functions:
pD = RD (pN ) , pN = RN (pD ) .
Then, if A2 and A3 form a codesharing alliance, the equilibrium variable proﬁts of A1 and the joint
variable proﬁts of A2 and A3 are:
¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢
π SC = pSC − cD qD pSC , pSC ,
1 D D N π SC = pSC − cxy − cyz qN pSC , pSC .
23 N D N
Proposition 1. Codesharing between A2 and A3 lowers ﬁnal prices for both the direct and non-
direct products (itineraries). That is, pS > pSC , and pS > pSC .
D D N N
Proof. Since equations (1) and (5) have the same form, while equations (4) and (6) diﬀer only
¡ ¢ ¡ ¢
in that (4) contains an extra positive term qN pS , pS , the reaction curves determining pS , pS
D N D N
¡ ¢ S SC
diﬀer from the reaction curves determining pSC , pSC only in that RN (pD ) is higher than RN (pD )
along the pN axis. Therefore RD (pN ) and RN (pN ) must intersect at a point that is higher and to
the right of the intersection point of RD (pN ) and RN (pN ) , implying pS > pSC and pS > pSC .
D D N N
Codesharing by A2 and A3 has an allocative eﬃciency eﬀect: it eliminates a double markup
existing between a bilateral monopoly for product N, lowering the ﬁnal price for N. This further has
a strategic eﬀect on A1, motivating A1 to lower its price for D. So in this case codesharing clearly
increases competition between D and N, beneﬁting consumers. Whereas the allocative eﬃciency
This is appropriate in the setting of this paper. For general models of vertical contracting that involve multilateral
bargaining in which the distribution of surplus is important, see, for instance, de Fontenay and Gans (2005), and
Inderst and Way (2003).
eﬀect aﬀects positively the joint proﬁts of A2 and A3, the strategic eﬀect has a negative eﬀect.
The incentive for codesharing between A2 and A3 also depends on possible savings in ﬁxed costs.12
In equilibrium, A2 and A3 will form codesharing alliance if codesharing increases their total joint
proﬁts. We thus have:
Remark 1. Assume that A3 is the only provider of nxy . Then, codesharing between A2 and A3
will occur in equilibrium if
π SC − kxyz > π S + π S − kxy − kyz .
23 2 3
As our linear-demand example in the Appendix shows, π SC can be either higher or lower than
π S + π S , depending on the parameter values. Thus, A2 and A3 can have the incentive to form an
alliance even without cost savings.
4 When only A1 oﬀers nxy
This situation corresponds to market structure M, with A1 oﬀering both D and nxy (i.e., u = 1).
4.1 Without Codesharing
We ﬁrst consider the equilibrium without codesharing. In this case, A1 will choose both pD and
r1 , while A2 will choose r2 ; and again the prices are chosen simultaneously. The variable proﬁt
functions of the two ﬁrms, A1 and A2, are:
π 1 = (pD − cD ) qD (pD , r1 + r2 ) + (r1 − cxy ) qN (pD , r1 + r2 ) , π 2 = (r2 − cyz ) qN (pD , r1 + r2 ) .
The equilibrium prices, pM , r1 , r2 , solve the ﬁrst-order conditions:
∂qD (pD , pN ) ∂qN (pD , pN )
qD (pD , pN ) + (pD − cD ) + (r1 − cxy ) = 0, (7)
∂qD (pD , pN ) ∂qN (pD , pN )
(pD − cD ) + qN (pD , pN ) + (r1 − cxy ) = 0, (8)
∂qN (pD , pN )
qN (pD , pN ) + (r2 − cyz ) = 0, (9)
where pN = r1 + r2 , and we let pM = r1 + r2 . These ﬁrst-order conditions again implicitly deﬁne
three reaction functions.
Notice that equations (2) and (9) have the same form, whereas equations (7) and (8) diﬀer from
equations (1) and (3) only in that there is an extra positive term in (7) and in (8). Using the same
Alliances may result in cost savings since alliance partners often jointly use each others facilities (lounges, gates,
check-in counters etc.), and may also practice joint purchase of fuel (Bamberger, Carlton, and Neumann, 2004).
¡ ¢ ¡ ¢
M M S S
reasoning in obtaining Proposition 1, we have pM , r1 , r2 >> pS , r3 , r2 . Therefore, without
codesharing, the equilibrium prices are higher when nxy is oﬀered by a ﬁrm that also oﬀers D, a
product competing with N, than when nxy is oﬀered by a single-product ﬁrm. This is because A1’s
incentive to raise prices is higher when it oﬀers both nxy and D than when it only oﬀers D.
Notice also that equations (8) and (9) diﬀer only in that there is an extra positive term in (8),
¡ M ¢ ¡ M ¢
which implies r1 − cxy > r2 − cyz > 0. Thus, unlike when A3 oﬀers nxy , where the price
markup for goods nxy and nyz are the same, here the markup for nxy is higher. Furthermore, when
A1 oﬀers both nxy and D, we have r1 > cxy .
The equilibrium variable proﬁts for A1 and A2, without codesharing, are
¡ ¢ ¡ ¢ ¡ M ¢ ¡ ¢ ¡ ¢ ¡ ¢
π M = pM − cD qD pM , pM + r1 − cxy qN pM , pM ,
1 D D N D N π M = pM − r1 − cyz qN pM , pM .
Let ΠM ≡ π M + π M be the equilibrium industry proﬁt under market structure M without code-
4.2 Comparing With Codesharing
Next, we consider the equilibrium with codesharing. The major diﬀerence between this case and
the case where A3 oﬀers nxy is that, now for the transfer price w1 in the codesharing agreement,
maximizing the joint proﬁts of A1 and A2 is the same as maximizing the industry proﬁt (and hence
w1 need not equal to cxy ), while previously w3 maximizes the joint proﬁts between A2 and A3 (and
hence w3 = cxy ).
Given any w1 agreed to by A1 and A2, the variable proﬁts of A1 and A2 are:
π 1 = (pD − cD ) qD (pD , pN ) + (w1 − cxy ) qN (pD , pN ) , π 2 = (pN − w1 − cyz ) qN (pD , pN ) .
The equilibrium prices pD (w1 ) and pN (w1 ) solve the ﬁrst-order conditions:
∂qD (pD , pN ) ∂qN (pD , pN )
qD (pD , pN ) + (pD − cD ) + (w1 − cxy ) = 0, (10)
∂qN (pD , pN )
qN (pD , pN ) + (pN − w1 − cyz ) = 0. (11)
Since the left-hand sides of equations (10) and (11) above are higher with higher w1 , and since w1
aﬀects pN directly while aﬀects pD indirectly, we expect that p0 (w1 ) ≥ p0 (w1 ) > 0.
The variable industry proﬁt is
Π (w1 ) = (pD − cD ) qD (pD , pN ) + (w1 − cxy ) qN (pD , pN ) + (pN − w1 − cyz ) qN (pD , pN )
= (pD (w1 ) − cD ) qD (pD (w1 ) , pN (w1 )) + (pN (w1 ) − cxy − cyz ) qN (pD (w1 ) , pN (w1 )) .
w1 = arg max Π (w1 ) ,
or w1 satisﬁes
∂qD ¡ MC ¢ ∂qN 0 ¡ MC
¢ ∂qN 0
(pD (·) − cD ) + w1 − cxy pN (·) + pN (·) − w1 − cyz p (·) = 0. (12)
∂pN ∂pN ∂pD D
¡ MC ¢ ¡ MC ¢
Let pMC ≡ pD w1
D , and pMC ≡ pN w1
N . Then, provided p0 (w1 ) ≥ p0 (w1 ) > 0, we have:
¡ MC ¢ ∂qD ¡ MC ¢ ∂qN 0 ¡ ¢ ∂qN 0
0 = pD − cD + w1 − cxy MC
pN (·) + pMC − w1 − cyz
N p (·)
∂pN ∂pN ∂pD D
¡ MC ¢ ∂qD ¡ MC ¢ ∂qN 0 ¡ ¢ ∂qN 0
< pD − cD + w1 − cxy MC
pN (·) − pMC − w1 − cyz
N p (·)
∂pN ∂pN ∂pN N
¡ MC ¢ ∂qD ¡ MC ¢ ∂qN ¡ MC MC
¢ ∂qN 0
= pD − cD + w1 − cxy − pN − w1 − cyz p (·) .
∂pN ∂pN ∂pN N
¡ MC ¢ ∂qD ¡ MC ¢ ∂qN
= pD − cD + w1 − cxy + qN p0 (·) .
∂q ∂q ¡ MC ¢ ¡ MC ¢
where the ﬁrst inequality is due to ∂pN < − ∂pN and p0 w1
D N N > p0 w1
D > 0, and the last
equality is due to equation (11). This implies
¡ ¢ ∂qD ¡ MC ¢ ∂qN
pMC − cD
D + w1 − cxy + qN > 0. (13)
Since w1 is chosen to maximize Π (w1 ) , the equilibrium variable proﬁts of A1 and A2, π MC and
π MC , satisfy
¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢
π MC + π MC ≡ ΠMC = pMC − cD qD pMC , pMC + pMC − cxy − cyz qN pMC , pMC .
1 2 D D N N D N
Therefore, when one of the codesharing partners also oﬀers product D, the codeshare partners
can negotiate an intermediate-good price that maximizes the industry proﬁt, subject to the con-
straint that both airlines will independently choose the ﬁnal prices for D and N. We now turn to
the comparison of equilibrium prices.
¡ MC ¢ ¡ MC ¢
Proposition 2. Assume p0 w1N > p0 w1
D > 0. Then codesharing lowers the price for
nxy , although it does not eliminate the double markup; and codesharing lowers ﬁnal-good prices.
That is, cxy < w1 < r1 , pMC < pM , and pMC < pM . Furthermore, ΠMC > ΠM .
D D N N
Proof. First, from the ﬁrst-order condition on w1 , equation (12), we must have w1 > cxy ;
otherwise the left-hand side of equation (12) would be positive, which is a contradiction.
¡ M ¢
Next, in the equilibrium without codesharing, r1 , pM , pM satisfy equations (7)-(9) with
¡ MC ¢
pM = r1 + r2 , while in the equilibrium with codesharing, w1 , pMC , pMC satisfy equations
N D N
(10)-(11) and inequality (13).
Therefore, the reaction functions determining the two equilibria have the same forms except
equation (8) and inequality (13), which determine, respectively, the optimal r1 and w1 , for given
(pD , pM ) . Since ∂pN < 0, these two conditions imply that the reaction function for w1 is lower
M MC M
than that for r1 . Consequently, w1 < r1 , pMC < pM , and pMC < pM . Furthermore, since w1
D D N N
maximizes Π (w1 ) but w1 6= r1 , we have ΠMC > ΠM . Q.E.D.
Therefore, even when A1 oﬀers both the direct ﬂight and a segment in the non-direct ﬂight,
codesharing between A1 and A2 still alleviates double marginalization and lowers ﬁnal prices,
although it does not eliminate double marginalization. To understand this result, suppose we start
at the equilibrium price under codesharing. Without codesharing, a slight increase in r1 above
w1 by A1 raises both pD and pN , which raises A1’s proﬁt from D but lowers both A1 and A2’s
proﬁts from N ; the proﬁt reduction for A2 is not taken into account by A1 when it raises r1 without
codesharing, but is taken into account by A1 and A2 when forming the codesharing agreement.
MC < r M . On the other hand, codesharing does not eliminate double markup, because
now w1 > cxy is chosen to maximize the industry proﬁt, given that A1 and A2 will compete in
D and N.
Proposition 3. With codesharing, equilibrium prices are higher when A1 oﬀers both nxy and
MC > w SC , pMC > pSC , and pMC > pSC . Furthermore,
D than when A3 oﬀers nxy . That is, w1 3 D D N N
industry proﬁt is higher under M than under S, or ΠMC > ΠSC .
MC SC MC SC
Proof. Since w1 > cxy while w3 = cxy , we have w1 > w3 . Comparing the ﬁrst-order con-
ditions determining pSC , pSC , equations (5) and (6), with the ﬁrst-order conditions determining
¡ MC MC ¢
pD , pN , equations (10) and (11), we see that the left-hand sides of (10) and (11) are higher due
to an extra positive term in equation (10) and to the fact that w1 > w3 . This implies that the
reaction functions deﬁned by equations (10) and (11) are higher than those deﬁned by equations
(5) and (6); hence pMC > pSC and pMC > pSC .
D D N N
Furthermore, since w1 > cxy = w3 , we have ΠMC > ΠSC . Q.E.D.
Proposition 3 makes clear that the eﬀects of codesharing depend on who oﬀers nxy , a key insight
of our analysis. Compared to the situation where a single-product ﬁrm oﬀers nxy , prices are higher
if the ﬁrm oﬀering nxy also oﬀers D. Also, the fact that ΠMC > ΠSC will be important for our
analysis later when both A1 and A3 can oﬀer nxy and codeshare partners are chosen endogenously.
When neither codesharing partner oﬀers D, ﬁxed cost saving is sometimes necessary in order
for airlines to be willing to form codesharing alliances. In contrast, when a codesharing partner
also oﬀers D, codesharing achieves highest possible industry proﬁt even without cost savings. In
fact, since from Proposition 2 ΠMC > ΠM , we have:
Remark 2. When A1 oﬀers both nxy and D, there is always incentive for A1 and A2 to form
a codesharing agreement, as long as kxyz ≤ kxy + kyz .
5 Both A1 and A3 Oﬀer nxy
We have so far studied situations where either A1 or A3 can oﬀer the product nxy , but not both
of them. We have seen that codesharing beneﬁts consumers by lowering ﬁnal-product prices. We
now consider market structure B, allowing both A1 and A3 to oﬀer the same service for XY, or
to produce the homogenous product nxy . As before, we assume that A1 and A3 have the same
constant marginal cost of producing nxy , which is equal to cxy ; but now we assume kxy = 0 so that
both ﬁrms have incentive to produce nxy even if Bertrand competition between them drives their
prices for nxy down to marginal cost.
5.1 Without codesharing
In this case, A1 chooses r1 for nxy and pD for D, A3 chooses r3 for nxy , and A2 chooses r2 for
nyz ; and all prices are chosen simultaneously. Competition for nxy between A1 and A3 implies that
the only equilibrium price for nxy is r1 = r3 = cxy , despite the fact that A1 also produces D.13
Therefore the equilibrium prices for D and N are the same as those when only A3 oﬀers nxy and
there is codesharing, or pB = pSC and pB = pSC . Interestingly, competition for nxy leads to the
D D N N
same outcome as if A3 codeshares with A2.
5.2 Comparing With Codesharing
With codesharing, A2 ﬁrst decides with whom to form a codesharing alliance. We assume that A1
and A3 will make simultaneous (two-part tariﬀ) contract oﬀers to A2, and A2 will form alliance
with the partner whose oﬀer results in a higher proﬁt for A2.14 Importantly, the supplier of nxy
that is not chosen as A2’s codesharing partner will no longer have any demand from consumers
and will thus be excluded from the market.
As is shown in Chen (2001), when a vertically integrated ﬁrm competes with another upstream ﬁrm in supplying
a homogeneous input to a downstream ﬁrm, the equilibrium input price will be equal to the marginal cost, if the two
competitors have the same marginal cost.
Again, the precise form of bargaining between Au and A2 is not crucial for our results; A2’s choice of codesharing
partner and the equilibrium prices will be the same under any form of eﬃcient bargaining.
If A2 contracts with A3, their joint variable proﬁt would be π SC , as in subsection 3.2. In this
case, the variable industry proﬁt is ΠSC = π SC + π SC .
If A2 contracts with A1, they will achieve a joint variable proﬁt that is equal to the industry
variable proﬁt, ΠMC . Since ΠMC > ΠSC from Proposition 3, A1 is willing to oﬀer A2 a contract
that yields a higher proﬁt for A2, comparing to the contract that A3 is willing to oﬀer A2. Hence
in equilibrium A1 and A2 will form a codesharing alliance, resulting in the equilibrium prices
¡ MC MC MC ¢ MC
w1 , pD , pN , which are determined by equations (10)-(12). Since w1 > cxy and pMC > i
pSC for i = D, N, we have:
Proposition 4. When both A1 and A3 oﬀer nxy , allowing codesharing leads to a higher price
for nxy as well as to higher ﬁnal prices for both D and N.
When both A1 and A3 can oﬀer nxy , competition between them lowers the price for nxy ,
resulting in lower ﬁnal prices for D and N. But if codesharing is allowed, since A1 also oﬀers
D, A2’s codesharing with A1 leads to a higher industry proﬁt than its codesharing with A3 (i.e.,
ΠMC > ΠSC from Proposition 3). Thus A1 has an advantage in competing with A3 to be selected
as A2’s codesharing partner.15 In equilibrium, A2 will codeshare with A1, and their alliance softens
competition for D and N, raising ﬁnal prices.
The possibility that codesharing can increase ﬁnal prices and harm consumers has been sug-
gested in the literature before. In particular, Brueckner (2003) conjectured that when codesharing
partners have overlapping services, “cooperation may result in collusive behavior, which leads to a
higher rather than a lower fare” (Brueckner, 2003, page 106). Our analysis provides a formal theory
of how anticompetitive codesharing can arise. Interestingly, while in our model codesharing by A1
and A2 does soften price competition, it nevertheless lowers ﬁnal prices if A1 is the only possible
intermediate-good provider (as Propositions 2 and 3 indicate); but when there is competition for
the intermediate good, codesharing causes prices to rise. The reason for this diﬀerence is that,
without codesharing, prices are diﬀerent under the two market structures: when A1 is the only
possible supplier for nxy , the price for nxy is high, leading to higher ﬁnal prices; whereas when both
A1 and A3 compete to supply nxy , the price for nxy is low, leading to lower ﬁnal prices. Therefore,
codesharing causes diﬀerent price changes under the two diﬀerent market structures.
This result shares the similar intuition to the result in Chen and Riordan (forthcoming), where a vertically
integrated ﬁrm is able to exclude an equally eﬃcient upstream producer through an exclusive supply contract with
a downstream competitor.
This paper has conducted an equilibrium analysis of codeshare alliances. The pricing incentives and
competitive eﬀects of a codesharing alliance depend on both the characteristics of the codesharing
partners and the presence (or absence) of competition to become a partner. If no codesharing part-
ner oﬀers a separate single-carrier product in the concerned market, codesharing leads to marginal
cost pricing for the intermediate ﬂight; otherwise it does not eliminate double marginalization. On
the other hand, if there is only a single potential codesharing partner for the intermediate good
(ﬂight), codesharing results in lower ﬁnal prices for consumers, even when it does not eliminate
double marginalization; but if there is competition in providing the intermediate ﬂight, codesharing
forecloses the competition and leads to higher ﬁnal prices for consumers. Our results highlight the
importance of endogenizing the formation of codesharing alliances in understanding their compet-
Our ﬁndings have interesting policy implications. To the extent that a codesharing alliance can
beneﬁt consumers without eliminating double marginalization, policy analysis would need to look
beyond the issue of double marginalization in evaluating the competitive eﬀects of codesharing. Our
analysis suggests that it is important to consider who the codesharing partners are and what the
competitive condition of the market is. In particular, in market segments that are more competitive,
there could be more danger that codesharing would harm consumers.
For convenience, our model abstracts from the possibilities that A1 and/or A3 may sell nxy
for consumers who just ﬂy between X and Y, and A2 may sell nyz for consumers who just ﬂy
between Y and Z. If we were to include these consumers in our model, our analysis would be much
more complicated. These consumers could have diﬀerent demands for nxy from the consumers
who purchase nxy to travel between X and Z, and codesharing might have other eﬀects such as
enabling airlines to engage in price discrimination. If either A3 or A1 alone oﬀers nxy , our result
that codesharing lowers prices likely would continue to hold: when codesharing lowers the price for
nxyz , a passenger travelling between X and Z through the indirect ﬂight would choose the codeshare
ticket rather than purchase nxz and nyz separately. Additional complication would arise if both A1
and A3 sell nxy . In this case, codesharing between A1 and A2 would still exclude A3 from serving
the consumers for whom nxy is an intermediate good, but it could not exclude A3 from serving
In their study of rivalry between strategic alliances, Zhang and Zhang (2006) also consider a model in which
alliance formation is endogenously determined.
the consumers who just ﬂy between X and Y. The separate availability of nxy and nyz could then
constrain the ability of A1 and A2 to raise the price for nxyz .17 It would be interesting for future
research to address such issues.
There are other directions for future research. For instance, according to the prediction of
our theory, codesharing would lower ﬁnal prices in markets where no codesharing partner oﬀers a
separate single-carrier product or the complementary ﬂight segment lacks competition; and it would
raise ﬁnal prices in markets where the complementary ﬂight segment has multiple competitors prior
to codesharing. This is a prediction that can potentially be tested in future empirical work.18 It
would also be desirable for future research to relax our strong simplifying assumption that the
intermediate good is homogenous when supplied by competing airlines.
Appendix: A Linear Demand Example
This appendix considers a class of demand functions that take the forms:
qD = 1 − pD + β (pN − pD ) , qN = 1 − pN + β (pD − pN ) ,
where β ∈ (0, ∞) is a measure of product diﬀerentiation. We have veriﬁed that for this example our
assumptions made for the paper are all satisﬁed. In what follows we solve the equilibrium under
each game form explicitly, and illustrate the competitive eﬀects of codesharing under diﬀerent
market structures. For convenience of computations, we assume that cD = cxy = cyz = 0.
Analysis under Market Structure S
Solving equations (1) and (4) simultaneously, we obtain,
2 + 3β 3 + 5β
N , pS =
D ¡ ¢. (A1)
6β + 2β 2 + 3 2 6β + 2β 2 + 3
Similarly, by solving equations (5) and (6) simultaneously we obtain,
2 + 3β 2 + 3β
N , pSC =
D . (A2)
8β + 3β 2 + 4 8β + 3β 2 + 4
However, if our model were further modiﬁed so that A3 could earn variable proﬁts from selling nxy as an
intermediate good, then not being able to do so due to the codesharing of A1 and A2 might make it not viable for
A3 to stay in the market in the presence of ﬁxed costs, and our result that codesharing leads to higher prices would
Our ﬁnding that codesharing does not eliminate double marginalization if a codesharing partner also oﬀers a
single-carrier product in the same market is consistent with the empirical evidence in Gayle (2006).
Thus, as in Proposition 1, we have
(β + 1) β (β + 1)2
pS − pSC =
D D ¡ ¢ > 0, pS − pSC = ¡
N N ¢ > 0.
2 6β + 2β 2 + 3 (β + 2) 6β + 2β 2 + 3 (β + 2)
Substituting the equilibrium prices back into each ﬁrm’s proﬁt function, we obtain:
S S (3β + 2)2 (β + 1) SC (3β + 2)2 (β + 1) SC (β + 1) 24β + 18β 2 + 8
π 2 +π 3 = ¡ ¢2 , π 23 = , Π = ,
2 6β + 2β 2 + 3 (3β + 2)2 (β + 2)2 (3β + 2)2 (β + 2)2
¡ 2 ¢ (A3)
¡ ¢ 8β + 8β + 2 − β (3β + 2) (β + 1)
π SC − π S + π S = ¡
23 2 3 ¢2 . (A4)
2 6β + 2β 2 + 3 (β + 2)2 (3β + 2)2
We note that π SC − π S + π S R 0 for β Q 3.261. Thus, if there is no saving in ﬁxed costs, the
23 2 3
incentive for codesharing only exists when β ∈ (0, 3.261) , consistent with Remark 1.
Analysis under Market Structure M
First, solving equations (7), (8) and (9) simultaneously, we obtain:
1 2 + 3β 1 4 + 3β
pM = ,
r1 = , M
r2 = , pM = r1 + r2 =
2 6β + 6 3β + 3 6 (β + 1)
Next, solving equations (10) and (11) simultaneously, we obtain,
¡ ¢ MC
MC 2 + 3β + 2 + 4β + 3β 2 w1 MC
2 + 3β + 3β (1 + β) w1
pN = , pMC =
D . (A6)
8β + 3β 2 + 4 8β + 3β 2 + 4
Next, substituting pMC and pMC into the industry proﬁt function when A1 and A2 codeshare, we
MC MC β(3β+2)2
solve for the w1 that maximizes the industry proﬁt: w1 = 2(β+1)(8β+9β 2 +4)
. We then obtain:
4 + 12β + 18β 2 + 9β 3 4 + 6β + 9β 2
N ¡ ¢ , pMC =
D ¡ ¢. (A7)
2 8β + 9β 2 + 4 (β + 1) 2 8β + 9β 2 + 4
Thus, as in Proposition 2, we have:
MC M MC (3β + 2) (β + 2)
w1 > cxy = 0, r1 − w1 = ¡ ¢ > 0,
3 8β + 9β 2 + 4 (β + 1)
β 4β + 3β 2 + 2
pM − pMC
D D = ¡ ¢ > 0, pM − pMC =
N N ¡ ¢ > 0.
8β + 9β 2 + 4 3 8β + 9β 2 + 4 (β + 1)
The industry proﬁts without or with codesharing under market structure M are
M 18β + 17 MC 24β + 33β 2 + 18β 3 + 8
Π = , Π = ¡ ¢.
36 (β + 1) 4 (β + 1) 8β + 9β 2 + 4
We thus have, as in Propositions 2 and 3:
2β + 1
ΠMC − ΠM = ¡ ¢ > 0.
9 8β + 9β 2 + 4 (β + 1)
MC β (3β + 2)2 SC
w1 = ¡ ¢ > 0 = w3 ,
2 (β + 1) 8β + 9β 2 + 4
3 (3β + 2) β 2
pMC − pSC =
D D ¡ ¢ > 0,
2 8β + 9β 2 + 4 (β + 2)
4β + 3β 2 + 2 (3β + 2) β
pMC − pSC =
N N ¡ ¢ > 0;
2 8β + 9β 2 + 4 (β + 1) (β + 2)
(3β + 2)2 (2β + 1) β 2
ΠMC − ΠSC = ¡ ¢ > 0.
4 (β + 2)2 8β + 9β 2 + 4 (β + 1)
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